Supercritical Contact Processes on $Z$

Abstract

In this paper we introduce a percolation construction which allows us to reduce problems about supercritical contact processes to problems about 1-dependent oriented percolation with density $p$ close to 1. Using this method we obtain a number of results about the growth of supercritical contact processes and the wet region in oriented percolation. As a corollary to our results we find that the critical probability for oriented site percolation is greater than (>) that for bond percolation.